## OPTION 3

Clinical Trial with Strata-Specific Event Rates and Unequal Group Allocation

Ref: Bernstein D and Lagakos SW: Sample Size and Power Determination for Stratified Clinical Trials J. Statist. Comput. Simul. 1978, Vol 8, pp 65-73

The program computes sample sizes and power for stratified clinical trials. It is assumed that cases are accrued into the trial uniformly over time and that the survival time distribution for a particular stratum and treatment is the 1-parameter exponential. The program allows accrual for a period of T time units and a follow-up period of tau time units. Particular features permit allocation of a fixed, but not necessarily equal, proportion of controls and experimental cases across each stratum and permits the exponential failure rate to vary among the strata although the failure rate ratio (controls/experimentals) is identical for all strata. The program computes either the necessary accrual rate to achieve a specified power or the power associated with a specified accrual rate.

The program makes the following assumptions:

- Patients are accrued uniformly into the trial at a rate of N per time unit for a total of T time units. Patients are randomized with a fixed but not necessarily equal probability to either the control or experimental group. The proportions randomized to either the control or experimental therapy are the same in each stratum. After the accrual period, patients are followed for a period of "tau" time units of "continued observation".
- The survival time distribution for the control group is exponential with hazard rate, lambda, specified by the user. However, these calculations are reasonably accurate for Weibull distributions with increasing or decreasing hazards. The hazard rate ratio (controls/experimental) determines the alternative hypothesis "delta". It is assumed the experimental treatment will improve survival so that delta is > 1.
- The trial can be stratified into from 1 to 15 strata of patients having different hazard rates. The user specifies the hazard rate for the controls in each stratum. The proportions of patients occurring in each of the strata are also specified; the sum of these proportions must equal 1.
- The program has been modified so that the test statistic variance conforms to that specified by Rubinstein, Gail and Santner. Thus, for 1 stratum, equal allocation and no loss trials, the two should give identical results.